Which number line represents the solution set for the inequality 2x - 6 2 6(x - 2) + 8?-1.5-1-0.500.51.5-1.5-1-0.500.51.55-0.500.51.5-1-0.500.51.5
Answers
Solve the inequality:
2x - 6 ≥ 6(x - 2) + 8
Operating the parentheses:
2x - 6 ≥ 6x - 12 + 8
Subtracting 6x:
2x - 6x - 6 ≥ - 12 + 8
Adding 6:
2x - 6x ≥ - 12 + 8 + 6
Simplifying:
- 4x ≥ 2
Dividing by -4 and changing the symbol:
x ≤ 2/(-4)
x ≤ -0.5
The solution in the number line starts at -0.5 and goes to the left with an arrow:
Related Questions
Real world compositionsWhat is the volume of a spherical balloon after 11 seconds if the radius of the balloon is increasing at 1.3 cm/sec? Round to the nearest tenth of a centimeter solve using composite functions
Answers
In this case we have two functions. The first one is the volume of the balloon and the other is the value of the radius. Both functions depend on the variable time.
Finding the functions to solve the problem, we have:
[tex]\begin{gathered} V(t)=\frac{4}{3}\pi r^3\text{ }^{}\text{ (First function)} \\ r(t)=1.3\cdot t\text{(Second function. Let us suppose that the initial radius is equal to zero)} \end{gathered}[/tex]Let us replace the second function in the first one to get a composite function. Doing so, we have:
[tex]\begin{gathered} V(t)=\frac{4}{3}\pi(1.3\cdot t)^3 \\ V(t)=\frac{4}{3}\pi(2.197\cdot t^3)\text{ (Raising the expression within parentheses to the power of 3)} \\ V(t)=2.93\pi\cdot t^3(^{}\text{ Multiplying constant terms)} \end{gathered}[/tex]Now, we can replace t=11 to find the value of the volume.
[tex]\begin{gathered} V(11)=2.93\pi\cdot(11)^3\text{ } \\ V(11)=2.93\pi(1331)\text{ (Raising 11 to the power of 3)} \\ V(11)=12248.88\text{ (Multiplying)} \end{gathered}[/tex]The answer is 12248.9 cm3 (Rounding to the nearest tenth of a centimeter).
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Determine whether the statement makes sense or does not make sense, and explain your reasoning.
.I read that a certain star is 10^5 light-years from Earth, which is 100,000 light-years.
Choose the correct answer below.
OA. The statement makes sense. The value of 10^5 is not 100,000.
OB. The statement makes sense. The value of 10^5 is 100,000.
OC. The statement does not make sense. The value of 10^5 is not 100,000.
OD. The statement does not make sense. The value of 10^5 is 100,000.
Answers
OB. The statement makes sense. The value of 10^5 is 100,000 is the correct answer.
How to expand exponential expressions?10^5 = 10*10*10*10*10 = 100,000
Repeated multiplication is expressed using exponential notation.
For instance, 10*10*10 can be expressed more briefly as 10^3.
The base is the number 10 in 10^3.
Exponent refers to the 3 in 10^3.
The exponential expression is known as the number 10^3.
You can learn how to conduct mathematical operations on an exponential expression or term by being familiar with its constituent parts' names.
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David watches Maria and Alma race electric trains around a track. Maria's train goes around the track in 10 seconds. Alma's train goes around the track in 12 seconds.
How long will it take for both trains to cross the finish line together the first time?
Answers
Answer:
60 seconds
Step-by-step explanation:
The LCM of 10 and 12 is
10 = 2 × 5
12 = 2² × 3
LCM = 2² × 3 × 5 = 60
Answer: 60 seconds
the anwser is 60 seconds
A model rocket is launched with an initial upward velocity of 113 ft/s. The rocket’s height h (in feet) after t seconds is giving by the following. h=113t-16t^2 Find all values of t for which the rockets height is 39 feet. Round your answer(s) to the nearest hundredth.
Answers
$4500 is deposited for 4.5 years in an account that pays 4.5% interest compounded monthly. What is the value of the account when the customer takes the money at the end of the 4.5 years?
Answers
Answer:
$5507.98
Explanation:
To find the value of the account, we use the compound interest formula below:
[tex]Amount\: at\: Compound\: Interest,A=P(1+\frac{r}{n})^{nt}[/tex]From the given information:
• Principal,P=$4500
,• Interest Rate, r=4.5%=0.045
,• Number of compounding periods, n=12 (Monthly)
,• Time, t=4.5 years
Substituting the given values, we have:
[tex]\begin{gathered} A=4500(1+\frac{0.045}{12})^{12\times4.5} \\ =4500(1+0.00375)^{54} \\ =4500(1.00375)^{54} \\ =\$5507.98 \end{gathered}[/tex]The value of the account when the customer takes the money at the end of the 4.5 years is $5507.98.
Your friend just purchased a new sports car for $32,000. He received $6,000 for his trade in and he used that money as a down payment for the new sports car. He financed the vehicle at 6.76% APR over 48 months. Determine the amount financed from the given information.
a.
$38,000
c.
$29746.15
b.
$32,000
d.
$26,000
Answers
Answer: C. $29,746.08
Step-by-step explanation:
6. The net profit margin ratio for two companies is modelled by
by
8x
3x - 1
for company B where x is the number of items sold in thousands. Sam is trying
5x
2x - 3
for company A and
to decide in which company he should buy stock so he is going to compare the ratios. He
has researched both companies and he knows that each produces over 25 000 items per
month.
(C: 25)
a) He wants to find out if theywould ever have the same ratio and if so when. How would
you tell him how to find this mathematically? What should he have found as his answer
to the question?
b) Which company has a higher ratio for 30 000 items sold? What is that ratio to the
nearest thousand for both companies?
Answers
We deduce that the ratios would be the same for 2111 sales.
Consequently, it is obvious that firm B has a better ratio for 30000 sales.
What is the concept of ratio and proportion?Majority of the explanations for ratio and proportion use fractions. A ratio is a fraction that is expressed as a:b, but a proportion says that two ratios are equal. In this case, a and b can be any two integers. The foundation for understanding the numerous concepts in mathematics and science is provided by the two key notions of ratio and proportion.
if A = B then
5x/(3x-3) = 8x/(3x-1)
24x^2 - 24x = 15x^2 - 5x
9x^2 - 19x = 0
x(9x - 19) = 0
x = 0 , not possible because zero number of sales is not possible
or
x = 19/9 thousands = approximately 2111
Therefore, we conclude 2111 sales, the ratios would be the same.
For the second part :
we substitute the value of x as 30000 in the equations to see which ratio is bigger
8*30000/3*30000-1=2.666 or 2.7
5*30000/2*30000-3=2.5
Therefore we can clearly see that the company b has a higher ratio for 30000 sales.
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Solve: 12/40 = 30/×
Answers
Given:
[tex]\frac{12}{40}=\frac{30}{x}[/tex][tex]\begin{gathered} x=30\times\frac{40}{12} \\ x=\frac{1200}{12} \\ x=100 \end{gathered}[/tex]Answer:
100Step-by-step explanation:
Solve:
12/40 = 30/×
it's a simple equation12 : 40 = 30 : x
x = 30 * 40 : 12
x = 1200 : 12
x = 100
PLEASE HELP ITS DUE SOON! I DONT GET ANY OF THIS! HELP WOULD BE MUCH APPRECIATED! NEED THIS DONE BEEN STUCK ON THIS FOR WAY TO LONG!
YOU WILL GET 100 POINTS IF YOU HELP! QUESTION DOWN BELOW!!!!!
Answers
1) [tex]BC \parallel EF, \angle 1=\angle 3[/tex] (given)
2) [tex]\angle 2=\angle 3[/tex] (corresponding angles)
3) [tex]\angle 1=\angle 2[/tex] (transitive property)
4) [tex]AB \parallel DE[/tex] (converse of corresponding angles theorem)
What is the smallest 3 digit number that is divisable by 2, 3, 4 , 5 and 6
Answers
The smallest 3 digit number that is divisible by 2, 3, 4 , 5 and 6 is 720.
How can the digit number that is divisible be caculated?Let us find the factors of the given numbers which are Factors of 2 are 1 and 2. then the factors of 3 are 1 and 3, the Factors of 4 are 1, 2 and 2, then the Factors of 5 are 12 and 5, then the Factors of 6 are 12, 2 and 3.
Then we can find the Lowest Common Factor of them as (1*2*3*2*2*5*2*3) which will give us 720.
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a casting weighted 148 lb out of the mold. it weighed 141 lb after finishing. what percent of the weight was lost in the finishing?
Answers
The amount of weight lost will be equal to 4.72%.
Percentage may be defined as a form of expressing a number as a fraction of hundred. To find the percentage of a number we divide the number by the total amount and then multiply the answer with hundred. The initial weight of the casting was 148 lb and the final weight is 141 lb. To find the percentage we use the formula
Percentage lost = [(Final weight - Initial weight)/Initial weight] × 100
Percentage lost = [(141 - 148)/148] × 100
Percentage lost = ( -7/148) × 100
Percentage lost = -0.0472 × 100
Percentage lost = -4.72% and since we write the absolute value therefore, Percentage lost = 4.72%.
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Simplify using order of
operations.
3 • 10 (9 + 1)²
Answers
Answer:
3000
Step-by-step explanation:
Parentheses - (9 + 1) = 10
Exponents - 10 x 10 = 100
Multiplication - 10 x 100 = 1000 then 1000 x 3 = 3000
D
A
S
Find the distance between the two points rounding to the nearest tenth.
(1,-3) and (-7,2)
Answers
Answer:
Length between two points is given as √(x1-x2)²+(y1-y2)², where x and y are the coordinates of the points.
Distance = √(1-(-7))²+(-3-2)²
= √8²+(-5)²
= √64+25
= √89
= 9.43
= 9.4 (nearest tenth)
Graph the line with slope 2/3
passing through the point (3,-1).
Answers
The graph of the line with slope 2/3 and passing through the point (3,-1) is given by
What is an equation of the line?
An equation of the line is a way of representing the set points which form a line in coordinates system. A basic equation of line is y=mx+c
We are given the slope of line as 2/3 and the line passes through the point (3,-1)
We substitute the values in slope intercept form we get
[tex]-1=\frac{2}{3}*3 +c\\c=-1-2\\c=-3[/tex]
Substituting the value of c in the original equation we get
y=2/3x-3
Hence the plot the graph of the above equation
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How many books must the publisher produce and sell so that the production cost will equal the money from sales
Answers
Step by step explanation:
Assuming x as the number of books, the function of production cost is:
[tex]C(x)=45240+9.25x[/tex]And the selling price function would be:
[tex]S(x)=25.5x[/tex]For rhe production cost to be equal to the money from sales we have:
[tex]\begin{gathered} 25.5x=45240+9.25x \\ 25.5x-9.25x=45240 \\ 16.25x=45240 \\ x=\frac{45240}{16.25} \\ x=2784 \end{gathered}[/tex]Answer:
The publisher must produce 2784 books
What is the slope of a line perpendicular to the line whose equation is 6x+8y=−128. Fully simplify your answer.
Answers
The slope of a line perpendicular to the line 6x + 8y = -128 is 4/3.
Given,
The equation of a line = 6x + 8y = -128
We have to convert this into standard form of linear equation, y = mx + b :
So,
6x + 8y = -128
Add -6x to both sides,
6x + 8y - 6x = -6x - 128
Now,
8y = -6x - 128
Divide 8 on both sides
8y/8 = (-6x - 128) / 8
We get,
y = -6/8x - 16
Here, this is in standard form of linear equation.
Here slope of line, m₁ = -6/8
We have to find the slope of line(m₂) which is perpendicular to the given line.
If the line is perpendicular, the slope(m₂) will be the negative reciprocal of the slope(m₁) of the given line.
That is,
Slope of line, (m₂)= -(m₁) = - (-8/6) = 8/6 = 4/3
That is, the slope of the line which is perpendicular to the given line is 4/3.
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ERROR ANALYSIS: Student A says there is no solution to the graphed system of equations. Student B says there is one solution. Which student is correct? Why?
Answers
Then, to solve the exercise, we need to know the slope of each line. The slope of a line is the measure of the steepness of a line.
The graph shows that the red line has a greater steepness than the blue line. Thus, the lines have different slopes. Also, two lines are parallel if they have the same slope. Since these lines have different slopes, they are not parallel.
Therefore, student B is correct because the lines are not parallel, so they will intersect.
Translate to an equation, then solve.The product of 2, and a number increased by 7, is – 36.
Answers
Let the number be r then
2r is the product of 2 and the number
2r + 7 is when the product is increased by 7
2r + 7 = -36
2r = -36 - 7
2r = -41
r = -41/2
= -20 1/2
I NEED HELP PLEASE!
Answers
Enter the ratio as a fraction in lowest terms
2ft to 40 in.
Answers
Answer:
[tex]\frac{3}{5}[/tex]
Step-by-step explanation:
2 feet is equivalent to 24 inches. (12 inches make a foot 2 x 12 = 24)
[tex]\frac{24}{40}[/tex] = [tex]\frac{3}{5}[/tex] Divide the top (numerator) and the bottom (denominator) by 8 to simplify.
to convert a decimal to do a fraction for the decimal over ______and multiply the numerator and denominator by _______and tell there is no longer a decimal in the numerator then___ your fraction
Answers
1) Let's proceed the steps
To convert a decimal to do a fraction for the decimal over one
Ex
0.5/1
And multiply the numerator and denominator by ten
Ex
5/10
(..) *until there is no longer a decimal in the numerator then simplify your fraction
Ex
1/2
Rationalise
(3+√2)/(√5+√3)
Answers
Rationalization of the surd [tex]\frac{(3+\sqrt{2} )}{(\sqrt{5} )+\sqrt{3} }[/tex] gives [tex]\frac{3\sqrt{5} -3\sqrt{3}+\sqrt{10} -\sqrt{6} }{2}[/tex]
What is surd?In mathematics surd refers to the root of numbers that do not have a perfect root. Surds are used to represent irrational numbers in square root, cube root and so on.
How to Rationalize (3+√2)/(√5+√3)The data given the question is
[tex]\frac{(3+\sqrt{2} )}{(\sqrt{5} )+\sqrt{3} }[/tex]
This is solved as follows;
[tex]\frac{(3+\sqrt{2} )}{(\sqrt{5} )+\sqrt{3} }[/tex]
Rationalizing the denominator
[tex]\frac{(3+\sqrt{2} )}{(\sqrt{5} +\sqrt{3} }*\frac{\sqrt{5} -\sqrt{3} }{\sqrt{5} -\sqrt{3} }[/tex]
multiplying out
[tex]\frac{3\sqrt{5}-3\sqrt{3} +\sqrt{10}-\sqrt{6} }{5-\sqrt{15} +\sqrt{15} -3}[/tex]
adding and subtraction when required
[tex]\frac{3\sqrt{5}-3\sqrt{3} +\sqrt{10}-\sqrt{6} }{5-3}[/tex]
[tex]\frac{3\sqrt{5}-3\sqrt{3} +\sqrt{10}-\sqrt{6} }{2}[/tex]
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In the diagram, .
Triangles G E F and J H I are shown. The length of side G F is 20 and the length of side I J is 10. Th elength of side F E is 40 and the length of side I H is 20.
To prove that the triangles are similar by the SAS similarity theorem, it needs to be proven that
Answers
In order prove that the triangles are similar by the SAS similarity theorem, it needs to be proven that A. J measures 60°.
What is SAS Similarity Theorem?The SAS Similarity Theorem states that two triangles are similar if their included angles are congruent and their two sides are proportionate to one other. Triangle congruence and resemblance are both criteria for SAS.
The triangles are congruent if two sides and the included angle of one triangle are equivalent to two sides and the included angle of another triangle.
In this case, the length of side FE is 40 and the length of side IH is 20. This gives a value of 60. Therefore, J should measure 60°.
In conclusion, the correct option is A.
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Triangles G E F and J H I are shown. The length of side G F is 20 and the length of side I J is 10. Th elength of side F E is 40 and the length of side I H is 20. To prove that the triangles are similar by the SAS similarity theorem, it needs to be proven that
J measures 60°.
J measures 30°.
I measures 60°.
I measures 30°.
Does the point (1, 0) satisfy the equation y = 7x + 1? yes no
Answers
To find out if the point (1,0) satisfy the equation we plug x=1 and y=0 into the equation:
[tex]\begin{gathered} 0=7\cdot1+1 \\ 0=8 \end{gathered}[/tex]since this is not true we conclude that th
f(x) = 4
this line is
vertical
O horizontal
O diagonal
O impossible to graph
Answers
f(x) = 4
this line is
O vertical
O horizontal
O diagonal
O impossible to graph
Can someone please help me graph this? It’s due in 5 minutes
Answers
An order relationship with greater than, greater than or equal to, less than, or less than or equal to between two algebraic expressions. The solution of inequality -3x+4≥10 is x≤-2
What is Inequality?An order relationship with greater than, greater than or equal to, less than, or less than or equal to between two algebraic expressions.
The given inequality is
-3x+4≥10.
To solve the above inequality
Subtract -4 from both sides.
-3x+4-4≥10-4
+4 and -4 we get zero.
-3x≥6
Divide by 3 on both sides
-x≥2
When negative sign is multiplied on both sides, the greater than or equal to symbol changes to lesser than or equal to.
x≤-2
Hence x≤-2 is solution for -3x+4≥10.
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Which equation is equivalent to
5x - 2(7x + 1) = 14x?
A. -9x - 2 = 14x
B. -9x + 1 = 14x
C. -9x + 2 = 14x
D. 12x 1 = 14x
Answers
Option A, -9x - 2 = 14x is the required equivalent equation for the equation 5x - 2(7x + 1) = 14x.
What are equivalent equations?
Equations with the same answer or solution are said to be equivalent. Comparisons between linear equations are common. When graphed, linear equations result in straight lines with a slope and a y-intercept. The characteristics that make a linear equation linear are crucial in establishing if two linear equations are equivalent. Although it may not seem like it at first, there are mathematical procedures to determine whether the equivalent equations will have the same solution.
To get equivalent equation of the given equation, we need to simplify it.
So, given equation
5x - 2(7x + 1) = 14x
Lets multiply -2 with 7x+1, we get
5x-14x-2=14x
it can be written as:
-9x - 2 = 14x
This is required equivalent equation.
Therefore, option A is correct answer
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Question 4Scott is constructing a taste of values that satisfies the definition of function.InpertOutput20320O16Which number could be placed in the empty cell so that the table of values satisfies the definition of afunction?
Answers
Remember that
A technical definition of a function is: a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
so
in this problem
the input value must be 3
answer is option CRachel and Nicole are training to run a half-marathon. Rachel begins by running 30 minutes on the first day of training. Each day she increases the time she runs by 3 minutes. Nicole’s training follows the function f(x)=5x+30, where x is the number of days since the training began, and f(x) is the time in minutes she runs each day. What is the rate of change in minutes per day for the training program that has the slowest rate of change?
............ minutes per day
Answers
The slowest rate of change that is the slowest for the training program is: 3 minutes per day.
What is the Rate of Change of a Function?In a given function that is expressed in slope-intercept form as .f(x) = mx + b, the rate of change of the function is represented as "m", while the starting or initial value is represented as "b" in the equation.
Given that Rachel increases the time she runs by 3 minutes for each day, then, the rate of change per day for the training program or Rachel is 3.
Given that the function .f(x) = 5x + 30 represents the minutes Nicole runs per day in the training program, then the rate of change is represented as "5" in the equation. This means that each day, Nicole increases her time of running by 5 minutes as compared to 3 minutes per day that Rachel increases her daily runs.
3 minutes per day is slower than 5 minutes per day, in order words, the slowest rate of change is therefore: 3 minutes per day.
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6. rule (x,y) ---> is the image similar to the original pre-image?
Answers
Here, we want to check for the relationship between the image and its pre-image
The pre-image is (x,y)
The image is (3x,3y+5)
As we can see, the pre-image is not similar
This is because the transformation applied to the two values are not same
Thus, we have that;
No, the image is not similar to the pre-image as the translations applied to both coordinates are not same
The pre-image was transformed by dilating the x-coordinate of the pre-image by 3 units while the y-coordinate was transformed by dilating the y-coordinate of the pre-image by 3 and translating it upward by 5 units